Final Project

Stat-515-002 (Spring 2024)

Group Number: 14

What is Project based on?

Our project revolves around a thorough examination of a dataset documenting motor vehicle collisions on county and local roadways within Montgomery County, Maryland. This dataset serves as the cornerstone for our investigation into the myriad factors that influence traffic accidents and their consequences. Through meticulous analysis and advanced statistical techniques, we aim to uncover insightful patterns and correlations that can inform proactive measures for enhancing road safety and mitigating accident risks.

In our endeavor, we transcend conventional data exploration by incorporating hypothesis testing and predictive modeling methodologies. By formulating and testing hypotheses pertaining to weather conditions, daylight, injury severity, vehicle types, distractions, and traffic control measures, we strive to unveil underlying relationships and trends within the data. Additionally, our predictive modeling efforts seek to anticipate injury severity and vehicle damage extent based on a diverse set of variables including collision type, vehicle movement, and speed limit. Through this comprehensive approach, our project aspires to deliver actionable insights that can empower stakeholders in making informed decisions aimed at fostering safer road environments and reducing the occurrence of motor vehicle collisions.

What’s our Goal?

Our goal is to deeply understand why and how motor vehicle collisions happen in Montgomery County, Maryland. By analyzing a vast amount of data on these accidents, we aim to uncover patterns, trends, and correlations that shed light on the factors contributing to crashes. Through this exploration, we seek to identify key variables such as weather conditions, road surfaces, vehicle types, and driver behaviors that play significant roles in accident occurrence and severity.

Ultimately, our aim is to use this knowledge to inform strategies and interventions that can enhance road safety and reduce the frequency and severity of motor vehicle collisions. By providing insights into the root causes and contributing factors of accidents, we aspire to empower policymakers, law enforcement agencies, and community stakeholders with the information they need to implement effective measures for preventing accidents and safeguarding lives on the roads of Montgomery County.

Research Questions :

hypo#1. is there any relation between weather condition, day light on injury severity

This test performs provided performs a chi-square test to determine whether there is a statistically significant association between weather condition, light condition, on injury severity, Here’s an explanation of why this test was conducted and what was observed:

  1. Weather and Light: This part of the analysis explores whether there’s a relationship between weather conditions (e.g., clear, rainy, snowy) and light conditions (e.g., daylight, dark with street lights, dark without street lights). For instance, the test can indicate whether certain weather conditions are more likely to occur in conjunction with specific light conditions. A significant result suggests that weather and light conditions are not independent of each other.

Chi-Square Test: The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. In this case, the variables of interest are weather condition, light condition.

Observation: By analyzing the contingency table generated from the data, which shows the frequency distribution of the combinations of weather condition, light condition, we can observe the following:

  • The contingency table provides counts of the number of accidents for each combination of weather condition, light condition.

  • The chi-square test is then applied to assess whether these variables are independent of each other or if there is a relationship between them.

Code 
# Contingency table of Weather, Light, and Injury Severity
contingency_table <- table(data$Weather, data$Light, data$Injury.Severity)

# Remove any empty dimensions
contingency_table <- margin.table(contingency_table, c(1, 2))


# Chi-square test of independence
chi_square_test <- chisq.test(contingency_table)
Warning in chisq.test(contingency_table): Chi-squared approximation may be
incorrect
# Print the test results
# print(chi_square_test)

Interpretation of Results: To analyze this, a Pearson’s Chi-squared test was conducted on the contingency table. The output indicates a significant relationship between these variables, with a very low p-value (p < 2.2e-16). This suggests that the observed frequencies of injury severity across different weather conditions and daylight statuses are unlikely to have occurred by chance alone, indicating a strong association between these factors.

visualization3 : Top 10 cars which involve in car cashes?

Code 
vehicle_counts <- data %>%
  group_by(Vehicle.Make) %>%
  summarise(count = n()) %>%
  arrange(desc(count)) # Sort by count in descending order

# Take the top N most common vehicle makes for better visualization
top_n <- 10 # You can adjust this value as needed

top_vehicle_counts <- vehicle_counts %>%
  top_n(top_n, count)

plot2 = ggplot(top_vehicle_counts, aes(x = reorder(Vehicle.Make, count), y = count)) +
  geom_bar(stat = "identity", fill = "blue") +  # Stacked bar plot with blue color
  labs(title = "Top 10 Most Common Vehicle Makes in Accidents",
       x = "Vehicle Make",
       y = "Number of Accidents") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        axis.text = element_text(size = 14)) +  # Adjust text size
  coord_flip() +  # Flip x and y axis
  ylim(0, max(top_vehicle_counts$count) * 1.1)
# plot2

Columns Used :

  • count: This variable represents the number of accidents associated with each vehicle make. It is the variable of interest that we are analyzing and visualizing in the plot.
  • Vehicle.Make: This variable represents the make or manufacturer of the vehicles involved in accidents. It serves as the predictor variable in this analysis, as it is used to group the data and determine the count of accidents for each vehicle make.

Explanation of the Code: This generates a bar plot showing the top 10 most common vehicle makes involved in accidents, with vehicle make names on the y-axis and the number of accidents on the x-axis. It uses dplyr to summarize and arrange the data, then ggplot2 for visualization.

hypo#2. Are certain types of vehicles more likely to be involved in collisions at night compared to during the day?

The code aims to determine whether certain types of vehicles are more likely to be involved in collisions at night compared to during the day. Here’s a clear interpretation of the analysis:

  1. Daylight Collisions: This subset represents collisions that occurred during daylight hours.

  2. Nighttime Collisions with Lights On: This subset represents collisions that occurred at night with lights on.

Chi-Square Test: A chi-square test of independence is performed to assess whether there is a significant association between vehicle types and the time of the collision (day or night).

Code 
# Subset data for collisions during the day and at night
collisions_day <- subset(data, Light == "DAYLIGHT")
collisions_night <- subset(data, Light == "DARK LIGHTS ON")

# Get the counts of each vehicle type for day and night collisions
counts_day <- table(collisions_day$Vehicle.Body.Type)
counts_night <- table(collisions_night$Vehicle.Body.Type)

# Perform chi-square test of independence
chi_square_test <- chisq.test(counts_day, counts_night)
Warning in chisq.test(counts_day, counts_night): Chi-squared approximation may
be incorrect
# Print the test results
# print(chi_square_test)

Interpretation of Results: To analyze this, a Pearson’s Chi-squared test was conducted comparing the counts of collisions involving different types of vehicles during the day and at night. The output indicates that there is no significant difference in the distribution of collisions across different types of vehicles between day and night, with a p-value of 0.2408. This suggests that the likelihood of different types of vehicles being involved in collisions is similar during both day and night.

hypo#3. Do drivers distracted by electronic devices have a higher rate of collisions compared to drivers distracted by other factors?

The analysis aims to determine whether drivers distracted by electronic devices have a higher rate of collisions compared to drivers distracted by other factors. Here’s a clear interpretation of the results:

  1. Driver.Distracted.By: This variable indicates the factor(s) distracting the driver at the time of the collision. In this analysis, it’s used to differentiate between collisions involving electronic device distractions and those involving other distractions.

  2. Collision Counts by Distraction Type:

  • counts_electronic: This represents the count of collisions where the driver was distracted by electronic devices.

  • counts_other: This represents the count of collisions where the driver was distracted by factors other than electronic devices.

Chi-Square Test: A chi-square test of independence is performed to assess whether there is a significant difference in collision rates between the two groups of drivers.

Code 
# Subset the data for drivers distracted by electronic devices
electronic_distracted <- subset(data, Driver.Distracted.By == "ELECTRONIC DEVICE")

# Subset the data for drivers distracted by other factors
other_distracted <- subset(data, Driver.Distracted.By != "ELECTRONIC DEVICE" & Driver.Distracted.By != "NOT DISTRACTED")

# Count the number of collisions for each distraction type
counts_electronic <- nrow(electronic_distracted)
counts_other <- nrow(other_distracted)

# Perform chi-square test
chi_square_test <- chisq.test(c(counts_electronic, counts_other))

# Print the test results
# print(chi_square_test)

Interpretation of Results: The question aims to determine if drivers distracted by electronic devices have a higher collision rate compared to those distracted by other factors. To analyze this, a Chi-squared test was conducted comparing the collision counts between drivers distracted by electronic devices and those distracted by other factors. The output indicates a significant difference between the two groups, with a very low p-value (p < 2.2e-16). This suggests that drivers distracted by electronic devices indeed have a significantly higher collision rate compared to those distracted by other factors.

hypo#4: Can we determine the effectiveness of different traffic control measures (Traffic.Control) in reducing collision rates? Which types of traffic controls are most effective in preventing collisions?

Column used:

  • Collision_Count: This variable represents the count of collisions for each type of traffic control. It is the response variable as it reflects the outcome of interest, i.e., the number of collisions categorized by the type of traffic control.
  • Traffic.Control: This variable represents different types of traffic controls (e.g., stop sign, traffic signal). It serves as the predictor variable as it is used to categorize and group the collisions based on the type of traffic control present at the collision location.

Graph :

Code 
# Subset the dataset to include only the required columns
traffic_data <- data[, c("Traffic.Control", "Injury.Severity")]
# Remove rows with any missing values
traffic_data <- na.omit(traffic_data)

library(ggplot2)
library(dplyr)

traffic_data[traffic_data == "N/A"] <- NA

# Remove rows with any missing values
traffic_data <- na.omit(traffic_data)

# Check if there are any missing values left
print(sum(is.na(traffic_data)))
[1] 0
collision_counts <- traffic_data %>%
  group_by(Traffic.Control) %>%
  summarise(Collision_Count = n())

# Calculate collision rates for each traffic control type
total_collisions <- nrow(traffic_data)
collision_rates <- collision_counts %>%
  mutate(Collision_Rate = Collision_Count / total_collisions)

# Statistical Analysis
# Perform chi-square test to compare collision rates between different traffic controls
chi_square_test <- chisq.test(traffic_data$Traffic.Control, traffic_data$Injury.Severity)
Warning in chisq.test(traffic_data$Traffic.Control,
traffic_data$Injury.Severity): Chi-squared approximation may be incorrect
# print(chi_square_test)
# Visualization
par(mfrow=c(1, 2))  # Set up a 1x2 plotting grid

# Create a bar plot using ggplot2
plot3 = ggplot(collision_counts, aes(x = reorder(Traffic.Control, -Collision_Count), y = Collision_Count)) +
  geom_bar(stat = "identity", fill = "skyblue") +
  labs(title = "Collision Counts by Traffic Control Type",
       x = "Traffic Control Type",
       y = "Collision Count") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))
# plot3

Interpretation of Results: To analyze this, a Pearson’s Chi-squared test was conducted between the types of traffic control measures and the severity of injuries resulting from collisions. The output shows a significant relationship between the two variables, with a very low p-value (p < 2.2e-16). This suggests that the effectiveness of traffic control measures in preventing collisions varies significantly across different types. However, further analysis would be needed to determine which specific types of traffic controls are most effective in reducing collision rates and severity of injuries.

per#3: Find the locations of crashes using the K-means algorithm?

Graph: Elbow Method - K means

The elbow method suggests that the optimal number of clusters is 2, it means that adding more clusters doesn’t significantly improve the clustering quality, and two clusters are sufficient to capture the main patterns in the data effectively.

Graph :

The two clusters represent two distinct geographical regions or patterns of accidents within the dataset. Red cluster might represent areas with high accident density, while the other cluster might represent areas with lower accident frequency.

###

Code 
# Load required libraries
#library(ggplot2)
#library(dplyr)

# Assuming your dataset is called 'location_data' and contains columns 'Latitude' and 'Longitude'

# Select latitude and longitude columns
#location_data <- data %>% select(Latitude, Longitude)

# Normalize data
#normalized_data <- scale(location_data)

# Initialize vector to store within-cluster sum of squares (WCSS)
#wcss <- vector()

# Iterate over different values of k
#for (i in 1:10) {
  # Apply K-Means algorithm
 # kmeans_model <- kmeans(normalized_data, centers = i)
  
  #Store within-cluster sum of squares (WCSS)
#  wcss[i] <- kmeans_model$tot.withinss}

# Plot the elbow curve
#plot4 = elbow_plot <- ggplot(data = data.frame(k = 1:10, WCSS = wcss), aes(x = k, y = WCSS)) +
  #geom_line(color = "blue") +
  #geom_point(color = "red") +
  #labs(title = "Elbow Method for Optimal K",
   #    x = "Number of Clusters (k)",
  #     y = "Within-Cluster Sum of Squares (WCSS)") +
  #scale_x_continuous(breaks = 1:10)

# plot4
#library(stats)
#library(ggplot2)

# Numerical columns for clustering
#numerical_cols <- c("Latitude", "Longitude")

# Subset the data with only numerical columns
#numerical_data <- data[, numerical_cols]

# Standardizing numerical data
#scaled_data <- scale(numerical_data)

# Determine the optimal number of clusters based on the elbow method
#num_clusters <- 2

# Perform k-means clustering with the chosen number of clusters
#kmeans_model <- kmeans(scaled_data, centers = num_clusters)

# Add cluster labels to the original dataset
#data$Cluster <- as.factor(kmeans_model$cluster)

# Visualize the clusters
#plot5 = ggplot(data = data, aes(x = Longitude, y = Latitude, color = Cluster)) +
  #geom_point() +
  #labs(title = "Clustering of Accidents based on Location") +
  #theme_minimal()

#plot5

visualization2 : How does the distribution of car accidents vary geographically?

Code

Columns used:

  • Latitude and Longitude: These variables represent the geographical coordinates of the crash locations. They serve as predictor variables as they are used to specify the locations where circle markers will be placed on the map.

Explanation of the Code: This utilizes the Leaflet package in R to generate an interactive map. It begins by loading Leaflet and then initializes a map object. Using latitude and longitude data from a dataframe named ‘data’, it places circle markers on the map to represent specific locations, like crash sites. Each marker includes a popup and label showing the associated report number. Finally, it prints the interactive map, allowing users to explore the locations and corresponding report numbers within the R environment.